Hybrid multi-agent optimization method of interpolation search
Maria Magdalina S. Karane, Andrei V. Panteleev · AIP conference proceedings · 2019
A new hybrid multi-agent algorithm of interpolation search is proposed to optimize the multi-extreme functions of many variables with a complex structure of level surfaces. This method is based on the construction of interpolation curves and uses the ideas of swarm intelligence. The novelty of the proposed approach consists in the application of various approximations of points sets. The construction of different interpolation polynomials allows adapting to a locally changing structure of the level surfaces of the objective function. A different role of leading points is also used to realize frontal search or deep search of an admissible solution set, thereby providing additional flexibility of the search strategy. Thus, the choice of the interpolation polynomial type and the points by which it is formed, implements two types of search — exploration and exploitation. On the basis of the algorithm developed, software that allows finding the conditional global minimum of functions of many variables is presented. With the help of this software, the efficiency of the algorithm on a set of standard test functions of two variables with a complex structure of level curves was explored. A series of 100 solutions to the problem were carried out and the statistical characteristics of the sample were calculated. Analysis of the obtained statistical characteristics showed high efficiency of the hybrid multi-agent method. The applicability of the algorithm on the applied technical optimization problem was demonstrated. The hybrid multi-agent method of interpolation search successfully coped with this task and the result was close to exact.